No, it's a fine analogy because the 23rd century is as much a real time period in Star Trek's universe as the 1970s are in our universe.
There is only one known Universe, one known physical reality.
It's the one we live in and are part of.
"Star Trek" takes place in a fictional continuity. For shorthand it's referred to as a "universe." The word usage does not signify that it exists on the same terms as or is equivalent in any way to what we call the Universe.
The phrase "a real time period in Star Trek's universe" is self-contradictory nonsense and drivel.
Any attempt to equate Trek's continuity with reality is logically absurd, untenable and unworthy of respect as a foundation for reasoning. And that is what "it's real in Trek's universe" does.